Iterative Learning Control Design Of Multiple Time-Delay Systems

Time-delay is a natural characteristic in dynamic process of material and energy. Control systems usually have multiple time delays, which might make system analysis complex and difficult. Moreover, the existence of multiple time delays also might lead to the instability and poor performance of controlled systems. Therefore, it is of theoretical and practical importance to study the multiple time-delay systems.Nonlinear control theory has become one of main field in control community. Nonlinearities that occur widely in almost all the fields may be caused by unavoidable nonlinear factors and nonlinear elements contained in controlled systems. Thus, the study of non-linear systems is meaningful to the development of control theory.Many complex processes have the characteristics of repetitive motion particularly in actual industrial applications. Iterative learning control is just suitable to those controlled objects with repetitive characteristics, which can achieve trajectory tracking in a finite time interval. However, the existing results mainly focussed on the systems without delays, and few dealt with the case of time-delay systems, particularly the multiple time-delays cases.In this thesis, we shall study the effects of multiple time-delays on the convergence of nonlinear systems by relevant theoretical analysis and simulations. The main contributions are outlined as follows:(1) We study iterative learning control of general model of non-linear multiple time-delay systems. By using PD-type iterative learning controller andλ-norm approach, we propose the sufficient conditions guaranteeing the global convergence of controlled systems. Numerical simulations are also presented to show the effectiveness of theoretical analysis.(2) The convergent conditions of iterative learning control for Hopfield neural network with time delays are also established, which ensure exact trajectory tracking in a finite time interval. Numerical simulations are also presented to show the validity of theoretical analysis.(3) Iterative learning control problem is also studied when there is fixed derivation between outputting trajectory and desired trajectory of non-linear multiple time-delay systems. For this case, we also derive the conditions guaranteeing the convergence of iterative learning control systems.